I remember things as far back as six months old, and thought that was completely normal until I was in high school and this very topic came up. It was then that I realized I was an oddity and my friends started telling me I had "freaky baby memory."

I remember the house that my grandparents moved out of when I was 6 months old. My mother often told this story: My grandfather made up a nonsense song that he sang to me as an infant and no one else ever sang it. He died when I was six months old. One day when I was about 2, I started singing the song out of the blue. She was cooking and said she nearly dropped a pan of biscuits right to the floor, it shook her up so much.
There is a photo of me in a swimsuit at 15 months old, taken outside by my mother. My sister was nearby, but not in the picture. My mother told me I was a "bathing beauty" and that captured my attention. I remember running inside and asking my father repeatedly, "Daddy, am I a bathing beauty?" (Yes, I talked WAY early.) All he wanted to do was get me out of the room, as he was laying on the couch, watching a western on TV. He finally assured me I was very pretty and I left him alone.

I have lots of memories from that time.
I have the "DVD/video memory" in that I can recall many memories as if I am watching a video. It always helped me in school. I could "replay" what the teacher had said, what had been on the film, even what I had read and what page it had been on. It has a down side too, though. Painful memories, such as being with my parents when they died, are as fresh as if they happened yesterday. They never fade with time, as they do for most people.
My sister has the same sort of memory and although I never discussed it with him, my late brother gave indications he had it too. I figure it's just an inherited trait.
My husband had an aunt who could recall amazing things. If someone mentioned an event, no matter how insignificant, she would say something like, "That happened on a Tuesday. It started off overcast, but cleared up by lunch. Joe was sick with the flu, but the rest of us were fine, so we headed into town to see a movie. They had a double feature..........." and so on. She had a mind like a steel trap.